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<p>This paper addresses the distributed permutation flow shop scheduling problem, motivated by an industrial application related to the manufacture of printed circuit boards. The goal is to minimize total tardiness while considering constraints such as no-waiting and sequence-dependent setup time. We have introduced an exact method based on mixed integer linear programming and three bio-inspired meta-heuristics. Specifically, we have explored the effectiveness of three bio-inspired meta-heuristics the artificial bee colony (ABC) , migratory bird optimization (MBO), and genetic algorithm (GA), to tackle the problem at hand. To enhance our approaches and minimize total tardiness, we incorporated local search improvement techniques. In addition to standard meta-heuristic formulations, we integrated specialized local search techniques, including the path relinking (PR) technique, variable neighborhood search (VNS), and the individual improvement scheme (IIS) procedures. This integration led to the development of three enhanced meta-heuristics: <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12065_2025_1057_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="57" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {ABC}_{{PR}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>ABC</mtext> <mrow> <mi mathvariant="italic">PR</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12065_2025_1057_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {MBO}_{{VNS}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>MBO</mtext> <mrow> <mi mathvariant="italic">VNS</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12065_2025_1057_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {GA}_{{IIS}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>GA</mtext> <mrow> <mi mathvariant="italic">IIS</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. Through simulation studies on various instances, we have demonstrated the superior performance of the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12065_2025_1057_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {MBO}_{{VNS}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>MBO</mtext> <mrow> <mi mathvariant="italic">VNS</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> algorithm, achieving a success rate of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12065_2025_1057_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(87.18\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>87.18</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> over other hybrid meta-heuristics.</p>

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Improved bio-inspired algorithms for scheduling distributed no-waiting flow shop with setup times

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Achraf Sayah,
  • Said Aqil,
  • Mohamed Lahby

摘要

This paper addresses the distributed permutation flow shop scheduling problem, motivated by an industrial application related to the manufacture of printed circuit boards. The goal is to minimize total tardiness while considering constraints such as no-waiting and sequence-dependent setup time. We have introduced an exact method based on mixed integer linear programming and three bio-inspired meta-heuristics. Specifically, we have explored the effectiveness of three bio-inspired meta-heuristics the artificial bee colony (ABC) , migratory bird optimization (MBO), and genetic algorithm (GA), to tackle the problem at hand. To enhance our approaches and minimize total tardiness, we incorporated local search improvement techniques. In addition to standard meta-heuristic formulations, we integrated specialized local search techniques, including the path relinking (PR) technique, variable neighborhood search (VNS), and the individual improvement scheme (IIS) procedures. This integration led to the development of three enhanced meta-heuristics: \(\hbox {ABC}_{{PR}}\) ABC PR , \(\hbox {MBO}_{{VNS}}\) MBO VNS , and \(\hbox {GA}_{{IIS}}\) GA IIS . Through simulation studies on various instances, we have demonstrated the superior performance of the \(\hbox {MBO}_{{VNS}}\) MBO VNS algorithm, achieving a success rate of \(87.18\%\) 87.18 % over other hybrid meta-heuristics.